You wish to test the following claim (HaHa) at a significance level of =0.10=0.1

Question

You wish to test the following claim (HaHa) at a significance level of =0.10=0.10. For the context of this problem, d=PostTestPreTestd=PostTest-PreTest one data set represents a pre-test and the other data set represents a post-test. Each row represents the pre and post test scores for an individual.

      Ho:d=0
      Ha:d0

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

pre-test post-test 55.3 42.8 50.7 72.7 33.5 38.7 35.6 56.1 26.6 -6.7 56.4 57.6 51.4 -0.7 34.2 56.2 61.8 47.3 39.9 45.7 54.3 7.4 51.1 36.6 46.1 45.2 37.5 28.8 31.7 23.5 26.6 25.7 44.5 15.3 48.2 53.4 46.1 69.8 57.1 27

Explanation / Answer

we use t-test and t=d-/(sd/sqrt(n))=7.31/(22.33/sqrt(20))=1.4640 with n-1=20-1=19 df

two tailed p-value=0.1595 ( using ms-excel =tdist(1.464,19,2)

(since alternate hypothesis Ha is two-tailed)

since p-value=0.1595 is more than alpha=0.1 , so we fail to reject H0 and accept H0.

following information has been generated using ms-excel

pre-test post-test d 55.3 42.8 12.5 50.7 72.7 -22 33.5 38.7 -5.2 35.6 56.1 -20.5 26.6 -6.7 33.3 56.4 57.6 -1.2 51.4 -0.7 52.1 34.2 56.2 -22 61.8 47.3 14.5 39.9 45.7 -5.8 54.3 7.4 46.9 51.1 36.6 14.5 46.1 45.2 0.9 37.5 28.8 8.7 31.7 23.5 8.2 26.6 25.7 0.9 44.5 15.3 29.2 48.2 53.4 -5.2 46.1 69.8 -23.7 57.1 27 30.1 mean= 7.31 sd= 22.32916 n= 20

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